Comments (0)

Transcript of IB Physics SL Option E: Astrophysics

IB Physics Option E:Astrophysics E2 Stellar radiationand stellar types E3 Stellar distances E4 Cosmology Energy source Luminosity Wien’s law and the Stefan–Boltzmann law Stellar spectra Types of star Parallax method Spectroscopic parallax Cepheid variables Absolute and apparent magnitudes The Big Bang model Olbers’ paradox The development of the universe The Hertzsprung–Russell diagram E2.1 State that fusion is the main energy source of stars. E2.2 Explain that, in a stable star (for example, our Sun), there is an equilibrium between radiation pressure and gravitational pressure. Students should know that the basic process is one in which hydrogen is converted into helium. They do not need to know about the fusion of elements with higher proton numbers. E2.3 Define the luminosity of a star. E2.4 Define apparent brightness and state how it is measured. E2.5 Apply the Stefan–Boltzmann law to compare the luminosities of different stars. E2.6 State Wien’s (displacement) law and apply it to explain the connection between the color and temperature of stars. E2.7 Explain how atomic spectra may be used to deduce chemical and physical data for stars. E2.8 Describe the overall classification system of spectral classes. Students must have a qualitative appreciation of the Doppler effect as applied to light, including the terms red-shift and blue-shift. E2.9 Describe the different types of star. E2.10 Discuss the characteristics of spectroscopic and eclipsing binary stars. Students need to refer only to single and binary stars, Cepheids, red giants, red supergiants and white dwarfs. Knowledge of different types of Cepheids is not required. E2.11 Identify the general regions of star types on a Hertzsprung–Russell (HR) diagram. Main sequence, red giant, red supergiant, white dwarf and Cepheid stars should be shown, with scales of luminosity and/or absolute magnitude, spectral class and/or surface temperature indicated.

Students should be aware that the scale is not linear.

Students should know that the mass of main sequence stars is dependent on position on the HR diagram. E3.1 Define the parsec. E3.2 Describe the stellar parallax method of determining the distance to a star. E3.3 Explain why the method of stellar parallax is limited to measuring stellar distances less than several hundred parsecs. E3.4 Solve problems involving stellar parallax. E3.5 Describe the apparent magnitude scale. E3.6 Define absolute magnitude. E3.7 Solve problems involving apparent magnitude, absolute magnitude and distance. E3.8 Solve problems involving apparent brightness and apparent magnitude. Students should know that apparent magnitude depends on luminosity and the distance to a star. They should also know that a magnitude 1 star is 100 times brighter than a magnitude 6 star. E3.13 Outline the nature of a Cepheid variable. E3.14 State the relationship between period and absolute magnitude for Cepheid variables. E3.15 Explain how Cepheid variables may be used as “standard candles”. E3.16 Determine the distance to a Cepheid variable using the luminosity–period relationship. Students should know that a Cepheid variable is a star in which the outer layers undergo a periodic expansion and contraction, which produces a periodic variation in its luminosity. E3.9 State that the luminosity of a star may be estimated from its spectrum. E3.10 Explain how stellar distance may be determined using apparent brightness and luminosity. E3.11 State that the method of spectroscopic parallax is limited to measuring stellar distances less than about 10 Mpc. E3.12 Solve problems involving stellar distances, apparent brightness and luminosity. E4.1 Describe Newton’s model of the universe. E4.2 Explain Olbers’ paradox. Students should know that Newton assumed an infinite (in space and time), uniform and static universe. E4.3 Suggest that the red-shift of light from galaxies indicates that the universe is expanding. E4.4 Describe both space and time as originating with the Big Bang. E4.5 Describe the discovery of cosmic microwave background (CMB) radiation by Penzias and Wilson. E4.6 Explain how cosmic radiation in the microwave region is consistent with the Big Bang model. E4.7 Suggest how the Big Bang model provides a resolution to Olbers’ paradox. Students should appreciate that the universe is not expanding into a void. E4.8 Distinguish between the terms open, flat and closed when used to describe the development of the universe. E4.9 Define the term critical density by reference to a flat model of the development of the universe. E4.11 Discuss problems associated with determining the density of the universe. E4.12 State that current scientific evidence suggests that the universe is open. E4.14 Evaluate arguments related to investing significant resources into researching the nature of the universe. Students should be able to demonstrate their ability to understand the issues involved in deciding priorities for scientific research as well as being able to express their own opinions coherently. E4.10 Discuss how the density of the universe determines the development of the universe. E4.13 Discuss an example of the international nature of recent astrophysics research. Students need to refer only to the principal spectral classes (OBAFGKM). It is sufficient for students to know that, if a Cepheid variable is located in a particular galaxy, then the distance to the galaxy may be determined. Students should be able to show quantitatively, using the inverse square law of luminosity, that Newton’s model of the universe leads to a sky that should never be dark. A simple explanation in terms of the universe“cooling down” is all that is required. This statement is included to give the students a flavor for the ongoing and complex current nature of research. They should be able to discuss relevant observations and possible explanations. They should recognize that, in common with many other aspects of our universe, much about the phenomena is currently not well understood.

Teachers should include dark matter, MACHOs and WIMPs. It is sufficient for students to outline any astrophysics project that is funded by more than one country. E1 Introductionto the universe The solar system and beyond E1.1 Outline the general structure of the solar system. E1.2 Distinguish between a stellar cluster and a constellation. Students should know that the planets orbit the Sun in ellipses and moons orbit planets. (Details of Kepler’s laws are not required.) Students should also know the names of the planets, their approximate comparative sizes and comparative distances from the Sun, the nature of comets, and the nature and position of the asteroid belt. E1.3 Define the light year. E1.4 Compare the relative distances between stars within a galaxy and between galaxies, in terms of order of magnitude. E1.5 Describe the apparent motion of the stars/constellations over a period of a night and over a period of a year, and explain these observations in terms of the rotation and revolution of the Earth. This is the basic background for stellar parallax. Other observations, for example, seasons and the motion of planets, are not expected. Orbits Planets Comets Asteroid Belt Planets orbit the sun in ellipses. Names in ascending distance from the sun in Astronomical units (distance from earth to the sun) and in Gigameters:Mercury: 0.387 AU / 57.9 GmVenus: 0.723 AU / 108.2 GmEarth: 1.000 AU / 149.6 GmMars: 1.524 AU / 227.9 GmJupiter: 5.203 AU / 778.3 GmSaturn: 9.539 AU / 1427.0 GmUranus: 19.182 AU / 2869.6 GmNeptune: 30.058 AU / 4496.6 Gm(Pluto: 39.440 AU / 5900.1 Gm) Nature of comets: Comets are made up of ice and dust. The ones we can see travel around the Sun in highly elliptical orbits taking from a few years to thousands of years to return to the inner Solar System. Typically comets are just a few kilometers across, which makes them very difficult to spot for most of their orbit. As they approach the Sun solar radiation vaporizes the gases in the comet and the characteristic comet 'tail' is formed. The tail of a comet consists of two parts: a whiter part made of dust, which always points away from the Sun, and a blue part consisting of ionized gas. Nature: It is occupied by numerous irregularly shaped bodies called asteroids or minor planets. Position: The asteroid belt is the region of the Solar System located roughly between the orbits of the planets Mars and Jupiter. Moons are objects that orbit planets. Names in descending radius (units are earth's radius)Jupiter: 11.19 earth's radiusSaturn: 9.41 earth's radiusUranus: 3.98 earth's radiusNeptune: 3.81 earth's radiusEarth: 1.00 earth's radiusVenus: 0.95 earth's radiusMars: 0.53 earth's radiusMercury: 0.38 earth's radius(Pluto: 0.18 earth's radius) There are 8 planets in the solar system (9 if you count Pluto) Stellar cluster Constellation A constellation is a distinctive pattern of stars that we see regularly on the earth's night sky. However, although these stars may form shapes that are recognizable to us here on Earth, they do not usually have any real link to each other, as they are often at different distances from the Earth, and are in fact very far away from each other. Orion: Stellar clusters are systems of stars that are held together by the gravity of their members. Due to their relatively well-known distances, and the similarities that tend to exist among their stars, stellar clusters play an important role in astrophysics. Some of the nearest stellar clusters are visible with the naked eye. Pleiades and Hyades in the constellation of Taurus A light year is the distance light travels through empty space in the course of one year. 1 light year = 9.46 x 10 m 15 This and other useful conversions are in the booklet: Values vary depending on stellar clusters and clusters of galaxies, this is because the distribution of objects is not uniform. However se can use our galaxy (The Milky Way Galaxy) and its corresponding cluster of galaxies to visualize the magnitude of these separations. Distance between the sun and other stars in our galaxy: 10 - 10 ly Distance between our galaxy and other galaxies in our cluster of galaxies: 10 - 10 ly 0 3 5 6 A difference of 6 orders of magnitude is present Night Year The stars appear to move during the night. Long exposure photographs show this: However it is not the stars that are moving, it is the earth's rotation that makes them appear to move in a circle. Stars rise above the eastern horizon and set below the western horizon. The stars appear to rotate around one point in the sky. Constellations appear to change their position slightly from one night only to return to the same position when a year has passed. The differences in position are accounted for by the revolution of earth around the sun. The "night" in your position will face a different part of the sky in the course of a year. A star forms out of a slowly condensing cloud of gas. As the pressure and density in the core increase so does the temperature. At a certain point a critical temperature is reached at which nuclear fusion (from topic 7) can occur.

The temperature and density of the plasma is enough to maintain the reaction. A great amount of energy is released. This occurs in all stars. When a star forms gravity is the dominant force (inward). As nuclear fusion begins, radiation pressure (outward) resists the inward pull of gravity and halts any further contraction. The star is then in equilibrium, it is a stable star.

The Sun is currently in this stable state. After 5000 million years all the fuel in the Sun will have been used up and, since it is no longer able to generate an outward radiation pressure, gravitational contraction will begin again. The luminosity (L) is the energy radiated into space per unit time. This energy is takes several forms, but the majority is released as electromagnetic radiation. The units are Watts (Joules per second). For example: The Sun has a luminosity of 3.8 x 10 Watts. 26 A star's apparent brightness (b) is described as the amount of energy that actually reaches us per unit area of the star.

The diminishing of apparent brightness obeys the inverse square law: doubling the distance from the star means the radiation intensity per unit area falls by one quarter. The units are watts per square meter. There's also a formula if luminosity and distance is known: L is the luminosity, sigma is the Stefan-Boltzmann constant (found in booklet), A is the area of the star (meters squared), and T is the temperature (Kelvin). Comparing two stars with the same area, one with temperature T and another with 2T: The energy released by the second star is 16 times greater ("burns faster" / "dies faster") compared to the first star. The law tells us that as stars get hotter their energy output increases quickly.

If two stars have the same temperature then the biggest one will have a greater luminosity because of the greater area. Wien's (displacement) Law relates the temperature of an object to the maximum wavelength at which it radiates energy, since as the temperature of an object increases the maximum wavelength will decrease. In this way, stars of different temperatures appear as different colors in the electromagnetic spectrum, with hotter stars appearing bluer and cooler stars appearing redder. Light is emitted in different amounts for all wavelengths but the maximum defines the "color" Light that has traveled through the atmosphere of a star has black lines in the spectrum. Light is a wave so it is subject to the Doppler effect. If the star is moving towards us (blue-shift) or away from us (red-shift) the frequency of light is shifted. The 7 classes are O, B, A, F, G, K and M. These divisions give an indication of the presence and strength of certain elements. You can remember with: "Oh Be A Fine Girl Kiss Me" or "Oh Boy An F Grade Kills Me".

O type stars are the hottest and M type stars are the coolest. The Sun is of classification G2. The classification can be related to a color description of the star (temperature-wavelength relation): O (blue), B (blue-white), A (white), F (yellow-white), G (yellow), K (orange) and M (red). Single stars Binary stars Cepheids Red giants Red supergiants White dwarfs A single star system consists of only one star. For example: the Sun. This contrasts with non-single stars systems A binary star system consists of two stars orbiting one another. They orbit around their common center of mass It is a star that pulsates in a regular cycle (period), with rapid brightening followed by gradual dimming. A red giant is a luminous giant star of low or intermediate mass in a late phase of stellar evolution. The outer atmosphere is inflated and tenuous, making the radius immense and the surface temperature low. The appearance of the red giant is from yellow orange to red, including the spectral types K and M. Red supergiants are supergiant stars of spectral type K or M. They are the largest stars in the universe in terms of volume. Betelgeuse and Antares are the best known examples of a red supergiant. A white dwarf is what some stars become and the end of their cycle. They are very dense: Sun's mass with earth size. Its faint luminosity comes from the emission of stored thermal energy. Eclipsing binaries Spectroscopic Binaries Eclipsing binary stars orbit around each other, but in a distinctive way that causes one star to eclipse the other as it passes in front of it, obscuring it from the observer's sight.

When the stars are next to each other, their maximum brightness can be seen by the observer, but their brightness, or magnitude, changes as the smaller star is behind or in front of the larger star. Some times the stars in a binary star system are too close to be distinguished by observation of the orbits. However, we can infer they are binary stars by looking at the stellar spectra. As one star moves, the absorption lines also seem to move (Doppler effect).The shift in binary systems behaves in a unique way. The main cepheid stars (Cepheid Variables) are in the instability strip. Others with longer period (not as noticeable) are in the red giant region. The apparent movement of close objects with respect to the background when an observer is moving is called parallax. A parsec is "The distance at which an object has a parallax of one arcsecond (1/3600 degrees)." 1 parsec = 3.26 light years = 3.09 x 10 m = 206 265 AU 16 By determining the parallax angle (in arc-seconds) you can determine the distance in parsecs to a star. The closer a star is to the Earth the greater the observed parallax. So for stars very far away the change is imperceptible. The greater the distance to the star, the bigger observer movement required for obtaining a discernible parallax. The observations from the Earth is limited to our planet's orbit around the Sun. Parallax angles smaller than about 0.01 arcsecond are very difficult to measure accurately from Earth, therefore stellar distances for stars further than around 100 parsecs cannot be measured from Earth. 1. A star has a parallax angle of 0.1 arcseconds. What is the distance to this star in light years? A = 32.6 ly

2b. With reference to 2b. state and explain whether or not the parallax method was used to find this distance. A = The method could not be used because the parallax would be too small to be observed from earth. Depends on luminosity and distance to a star. Stars may have the same apparent magnitude but be different distances away. The apparent magnitude, m, is a measure of how bright a star appears to an observer on earth. It has no units.

The scale was developed in ancient times. Magnitude 6 was the dimmest visible star, with new devices the scale was extended. Since the scale is logarithmic, a magnitude 1 star is 100 times brighter than a magnitude 6 star, i.e. an increase in each step on the scale is equal to a decrease in brightness of 2.512 and (2.512) 100. The absolute magnitude, M, of a star is the apparent magnitude of the star at a distance of 10 pc from Earth. In other words, it is a measure of how bright a star would appear to an observer on earth if the star was located at a distance of 10 pc form earth. Where m is the apparent magnitude, M is the absolute magnitude and d is the distance in parsecs. lg is the base 10 logarithm. 1a. The star Vega has an apparent magnitude of +0.03 and has an absolute magnitude of +0.58. Determine the distance to the star in light years. A = 25.3 ly 1b. Considering your answer in 1a. Determine the luminosity of the star considering an apparent brightness of 0.03 W m .A* = 8.74 x 10 W -2 16 2. Star A has an apparent magnitude of +1. Star B has an apparent magnitude of +6. Given that the apparent brightness of star A is 5.00 W m determine the apparent brightness of star B.A** = 0.05 W m -2 -2 *Using the formula: **Using the fact that a difference of 5 values is approximate to a 100 fold increase in brightness. The stars in the lower right have the smallest masses. As we go from the bottom right to the top left part of the main sequence stars increase in mass. The top left stars are the ones with greater mass. Knowing the spectrum of a star can lead to an estimate of its luminosity (or alternatively absolute magnitude) using the HR diagram. Spectroscopic parallax assumes that the relationships of close stars of the same type are the same relationships of distant stars. We use the inverse square law, which states that a star's apparent brightness decreases with the square of its distance. The resulting expression can give the answer in AU easily, just make the distance to the sun equal 1 AU. Spectroscopic parallax is only accurate enough to measure stellar distances of up to about 10 Mpc.

This is because the star has to be sufficiently bright to be able to measure the spectrum, which can be obscured by matter between the star and the observer. Even then there can still be uncertainty in determining its luminosity, and this uncertainty increases as the stellar distance increases. 1. A star has a luminosity of 10 Ls. It has an apparent brightness of 5.0 x 10 W m . Determine the distance to the star. Assume the apparent brightness of the sun is 1.3 x 10 W m . Answer is parsecs assuming 1 pc = 2.1 x 10 AU When the units in the y-axis of the HR diagram is Luminosity (L) it is generally given in luminosity of the sun (Ls). 3 6 -10 -2 -2 A = 7700 pc b is apparent brightness of the star,L is luminosity of the starand d is distance in meters To use the data of the HR diagram easily we need expression that only needs L in Ls (that way we don't need the value of Ls). To get an expression we substitute the values of the star and the sun in the previous formula to get two expressions. We then divide the two resulting expressions and isolate distance: 5 The variations happen generally at the end of the stars life, they pulsate with variations in size, temperature and brightness. They are also called Cehpeid stars When we observe another galaxy, we can assume that all its stars are around the same distance from the Earth. A source of known luminosity in that galaxy enables us to make comparisons with all the other stars in the galaxy to determine their luminosity. Cepheid variable stars provide us with such a benchmark, known in astronomy as a "standard candle". By observing the period of any Cepheid, you can deduce its absolute brightness/luminosity. Then, using known formulas from the booklet you can get the distance. 1. The star W Geminorum is a Cepheid variable and has a period of oscillation of 7.91 days. It has an average apparent magnitude of 7.16 (average of the maximum and minimum observed apparent magnitudes). Determine the distance to the Cepheid variable considering the relationship: A = 1590 pc Isaac Newton believed gravity demands that the Universe be without a center or an edge, and of infinite extent in all directions.

According to Newton, a finite and bound Universe would 'fall down into the middle of the whole space, and there compose one great spherical mass'. Olbers deduced that Newton's model of the sky leads to a contradiction: If you were to look in any direction in the sky, your line of sight would eventually hit on a star's surface and the sky would be infinitely bright. Then why is the night sky dark? Quantitative analysis Infinite in space Infinite in time Static Uniform The amount of light we see from stars some distance r from Earth can be calculated by multiplying the number of stars N that distance away, multiplied by the intensity I of each star. We assume uniform density of stars. N increases as r increases since N = constant × rThe intensity of light follows the Inverse-Square Law: I = constant × r There are more stars in the r ringthan in the r ring. 2 2 -2 2 1 Multiplying N and I cancels r with r , leaving a constant value for the intensity at some distance r. However, since the Universe is assumed infinite, this constant value must be added an infinite number of times, implying that the Universe must be infinitely bright. -2 2 A bright night sky is consistent with the inverse square law: The universe just is. There is no beginning.There is no end.Light has traveled to all points in the universe already. In an infinite Universe, he believed, 'the fixed stars, being equally spread out in all points of the heavens, cancel out their mutual pulls by opposite attractions.' The density must be uniform, or at least considerably uniform, in order to cancel out their mutual pulls by opposite attractions.

A constant density C can be assumed (stars per unit volume). The greater the volume the greater the amount of stars. Unchanging positions in the sense that there is no drastic displacement of stars and galaxies.

The universe in static equilibrium from all balancing forces. Consider a shell like volume of small width surrounding earth. The further the ring is from earth the greater the volume and therefore the greater the amount of stars (because of the constant density C.) Qualitative analysis It is tempting to assume that the inverse square law explains Olbers' paradox. However the distance of the stars and the inverse square law is irrelevant because that is balanced by the fact that the bigger the distance the more stars you will find at that distance. The resulting effect will make the brightness dependent on only the amount of stars/extent of the universe. Features in spectra from distant galaxies are shifted towards the red end of the spectrum (red shift). Red shift indicates that the objects are moving away from us. That leads scientists to conclude that the Universe is expanding. Another observation is that the further away the objects are the faster they are moving away from us. If the universe is expanding, is it expanding into empty space? The answer is no because both time and space are expanding and originated from the singularity from the Big Bang. If all galaxies are traveling away from each other at high speed, there must have been a point way back in the past when the entire Universe was concentrated in a single point. The term "the Big Bang" reffers to the creation event, when space and time originated. One of the hardest concepts to grasp is that the Universe is everything that there is, all the matter and energy, and dimensions. There is no 'outer edge' to the Universe, and it is not expanding into a void. This is because the dimensions that we normally use here on Earth are not valid when we consider the Universe. According to the Big Bang theory, the early Universe was an extremely hot place. If this were true, the Universe should be filled with radiation that the remnant heat left over from the Big Bang. This relic radiation is known as the cosmic microwave background (CMB). Two scientists Arno Penzias and Robert Wilson, were using a 6 meter microwave horn antenna to calibrate radio sources. The antenna had originally been designed to communicate with satellites and, by chance, operated in a very narrow band. Through all their observations a consistent offset in the temperature of the system of 3.3 K was observed.

They discussed the problem with leading scientists. They then used more sensitive equipment and the group realized the nature of the emission and that it represented an afterglow of the Big Bang. Penzias and Wilson received the Nobel Prize for physics in 1978 for their findings. Thus, if we know how old the Universe is and its expansion rate, we can also estimate what its current thermodynamic temperature must be, and consequently its radiation frequency. Scientists have calculated that the expansion of the Universe has led to a background radiation of a temperature of 2.73 K (the expansion made the universe "cool down"), which falls into the microwave region of the temperature spectrum. It corrects the infinite universe (time and space) supposition: The momentum of expansion and gravity are the two forces that determine the shape of the universe. Therefore the amount of mass in the universe has an effect in it. We therefore have 3 scenarios. Flat Open Closed If there is sufficient mass, then the gravity of the material will inevitably stop the expansion of the Universe, causing it to eventually collapse in on itself. This is referred to as a 'closed' Universe. A 'flat' Universe is one in which there is exactly the right amount of mass to stop expanding at some point in the future, but not enough to cause a contraction. Many scientists view this as an aesthetically pleasing solution. When scientists refer to an open Universe, this refers to the prospect of there not being sufficient mass to stop its expansion, which will continue forever. The critical density is the minimum density that ensures that the Universe could not expand forever, but will not collapse back on itself either.

"It is the density required for a flat development of the universe." If c is the critical density and D is the actual density: D > c, a closed universeD = c, a flat universe D < c, a open universe Current scientific evidence suggests that the universe is open. There are things we can't see/measure/detect that may or may not contribute to the mass of the universe. We can only see 10% of the universe. Dark Matter MACHOs WHIMPs Scientists have been accumulating evidence that there is a form of matter in the Universe that cannot be seen (doesn't interact with light). Maybe it is not made up of ordinary material in the form of protons, neutrons and electrons. They estimated the mass of distant galaxies by measuring the speed of their rotation. They found that their estimates of the mass of these galaxies are larger than can be explained purely by the presence of stars, gas and dust. There must be something else present, and they have given it the name 'dark matter'. Possible explanations for dark matter: MACHOs (MAssive Compact Halo Objects). These are objects that have a mass that is less than one twentieth of our Sun, and which consequently shine only dimly. They are not luminous enough to be directly detectable by our telescopes. They are made of ordinary matter. MACHOs may sometimes be black holes or neutron stars as well as brown dwarfs or unassociated planets. White dwarfs and very faint red dwarfs have also been proposed as candidate MACHOs. Scientists also speculate that new forces or new types of particles could make up much of the dark matter. They have called these particles WIMPs, or Weakly Interacting Massive Particles, which could have been produced shortly after the Big Bang. WIMPs do not interact through electromagnetism and therefore they cannot be seen directly. However they do interact with gravity. This combination of properties gives WIMPs many of the properties of neutrinos, except for being far more massive and therefore slower. And it is not known if neutrinos have mass. In 1997, cosmologists discovered that supernova explosions in distant galaxies showed that instead of the expected deceleration in the rate of the expansion of the universe, it appeared that the expansion was in fact accelerating. The ISS (International Space Station) The Hubble Telescope ISS HST HST's observations have led to breakthroughs in astrophysics, such as accurately determining the rate of expansion of the universe. The Hubble Space Telescope was built by the United States space agency NASA, with contributions from the European Space Agency (ESA), and is operated by the Space Telescope Science Institute. ESA agreed to provide funding and supply one of the first generation instruments for the telescope, as well as the solar cells that would power it, and staff to work on the telescope in the United States, in return for European astronomers being guaranteed at least 15% of the observing time on the telescope The International Space Station (ISS) is a habitable artificial satellite in low Earth orbit. ISS components have been launched by American Space Shuttles as well as Russian Proton and Soyuz rockets. The ISS serves as a microgravity and space environment research laboratory in which crew members conduct experiments in biology, human biology, physics, astronomy, meteorology and other fields. NASA is the National Aeronautics and Space Administration of USAESA is the European Space AgencyJAXA is the Japan Aerospace Exploration AgencyCSA is the Canadian Space Agency Answer coherently and clearly to the following questions: Positive aspects of investing significant resources to investigating the nature of the universe Negative aspects of investing significant resources to investigating the nature of the universe Understanding the nature of the universe helps shed light on philosophical questions: Why are we here? Is there other intelligent life in the universe?It is a fundamental and interesting area of mankind as a whole.Has the potential for improving quality of life for human beings because of subsequent technological developmentsOur planet may become inhabitable in the future Money could be better spent on providing food, shelter and medical care to the millions of people suffering from hunger, homelessness and disease right now.We might be able to get better returns from medical research than astronomical research.Its better to fund a great deal of small diverse research than putting lots of funding into one field.Is the information gained really worth the cost? Explain, giving one clear reason, why investing a significant amount of resources to investigating the nature of the universe may not be ideal to humanity. State a reason why it could also be beneficial to increase the investing amount to investigate the nature of the universe. What is produced What actually reaches us The spectrum of a star, therefore, displays a massive number of absorption lines, which reveal the composition of the star. They correspond to selective absorption of the radiation at specific wavelengths due to the various elements existing in the stellar atmosphere. Mass in the Main Sequence The scales The mainregions Cepheid stars in the diagram The HR diagram organizes information of known stars in a consistent and organized way. We can classify stars or obtain information from the diagram. The diagram The y-axis can be luminosity in solar luminosity units (Ls) and/or the absolute magnitude (M) that will be discussed in Topic E3. The scales in both axes are logarithmic, each "unit step" corresponds to a change of orders of magnitude or powers of a number . The scales are not linear! The axes The x-axis can be stellar class (OBAFGKM) and/or the stars surface temperature (T) in Kelvin. Main sequence, white dwarfs, giants and supergiants. Labeled in the diagram: The star Cephel gives the name to the Cepheid stars (Cephel is one). "Cepheid variable" is another way to designate Cepheid stars. Depends on luminosity and distance to the star. Apparent magnitude The magnitude numbers are bigger for faint stars, and magnitudes are negative for very bright stars. Scale and relationships. 5 ~ ~ Most stars are much further away than this, so the absolute magnitude of stars is usually brighter than their apparent magnitudes. By making the distance constant for all stars (10 pc) the brightness now only depends on luminosity, therefore it can be substituted for luminosity on HR diagrams. The following relationship holds: Remember Apparent magnitude is how bright a star appears to an observer on earth, it has no units.

Apparent brightness is the amount of energy per second that actually reaches us on earth per unit area. "Brightness" in this case refers to apparent brightness. Formula Remember than an increase of one unit of apparent magnitude equals a decrease of 2.512 in apparent brightness. The formula for two stars is the following: (not in booklet) 3. Star A has a greater apparent brightness than Star B. The difference between their apparent magnitudes is 1. Given that star B has an apparent brightness of 1.00 W m . Determine the apparent brightness of star A. -2 A = 2.51 W m . -2 We can assume that the star is a main sequence star if no further information is available. Formula HR diagrams with absolute magnitude (M) If the HR diagram or problem gives the absolute magnitude (M) instead of the luminosity (L) then the previously used formula can be used to get the distance (in pc): Some stars have period of a few days others have a longer period. Graph/formula may appear in the exam. Notice the logarithmic scales. Remember that absolute magnitude and luminosity are basically different measures of the same thing so the relationship holds for both, it can also be called the Period-Luminosity relationship: So M and the period follow an exponential relationship. Using logarithmical scale we can determine the values of M (or L) from the period. Some Cepheid variables are close to Earth, so we can determine the distance using the parallax method.

We then use the distance (d) and apparent brightness (b) to determine the luminosity (L). Finding the relationship We then graph the data. Finite time Finite space This is because the universe is 13.7 billion years old (from the Big Bang to now) as calculated by the expansion velocity. It puts the start of the universe at a finite time in the past. Therefore only light from stars that are closer than a certain distance can be seen: all the stars that are further away than 13.7 billion light years we can't see, because their light has not had time to get here yet. It establishes that space has a finite nature and possibility a finite amount of stars. It establishes that space is currently expanding and therefore the separation between places with stars and places with no stars are increasing. It can be measured by focusing image of the star to an electronic detection device, such as a CCD in a camera, placed perpendicular to the direction of the star. The detector will record how much energy strikes its surface each second. Measured